Square-mean weighted pseudo almost automorphic solutions for stochastic semilinear integral equations

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In this paper, we introduce the concept of S²-weighted pseudo almost automorphy for stochastic processes. We study the existence and uniqueness of square-mean weighted pseudo almost automorphic solutions for the semilinear stochastic integral equation x(t)=∫₋∞ᵗa(t-s)[Ax(s)+f(s,x(s))]ds+∫₋∞ᵗa(t-s)φ(s,x(s))dw(s), t, where a∈ L¹(R₊), A is the generator of an integral resolvent family on a Hilbert space H, w(t) is the two-sided Q-Wiener process, f,φ: R× L²(P,H)→ L²(P,H) are two S²-weighted pseudo almost automorphic functions.